262 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
science, and reading which have been given to students from different nations. Out of 41 countries participating
in the Third International Math and Science Study TIMSS, 8th grade students from the US ranked 28th
and 17th respectively in math and science.
2
On a positive note, 4th graders from the US, in results recently
released, scored above the average in math and near the top in science.
3
As a result of these disappointing results from TIMSS and the testing that preceded TIMSS, sev-
eral reports about US schools have been written criticiz- ing not only the poor results but also the high costs and
fairness of the system.
4
Other than the need for an educated workforce, another reason for governmental interest in such studies
as TIMSS is the movement in governments to be more efficient when spending from public coffers. Put simply,
governments are trying, given their tight budgets, to obtain more for each dollar spent on public activities.
The current fiscal tightening in Europe as well as in Washington are but two examples of this phenomenon.
Policy makers want least cost educational strategies which are effective in enhancing student learning.
As a result, educators have proposed that reforms be made in the US school system. Without the knowledge
of what causes students to learn, changes are likely to be ineffective. Educational production functions, because
they provide estimates of the determinants of student performance, provide insights into the factors which
have been discussed by researchers as likely to improve performance on achievement tests. In order to provide
this information and fill a gap in the economics of edu- cation literature, panel data are employed to estimate the
determinants of achievement in mathematics. The data set used in our study, the National Education Longitudi-
nal Study of 1988 NELS, is a nationally representative data set, including features related to high school stu-
dents, their schools, parents, and teachers. The variables we have chosen to emphasize are those related to the
time students spend in their math classes along with the time they spend doing math homework.
The issue of ‘omitted variable bias’ arises frequently when cross-sectional or single time series data are
employed. In order to specify and analyze economic hypotheses correctly, a researcher has to include vari-
ables that are thought to influence and explain the out- come. When one or more of these variables are omitted
from the behavioral relationship, usually due to the lack of data or a specification error, the effects of these omit-
ted variables appear through the error term and the likely outcome is biased coefficient estimates. In studies of the
2
See The Economist 1997, p. 21, for a list of the countries and their math and science scores.
3
See Kronholz, 1997.
4
See for instance, US Department of Education 1984.
determinants of achievement, omitted variables in cross- sections include, among others, innate ability, and motiv-
ation. If the effects of the omitted variables are constant over time or if they are the same across all individuals
at a given point in time, the bias can be eliminated using panel data estimation techniques. Panel analysis auto-
matically lessens the degree of this bias by excluding variables that are specific to the individual but constant
over time and including variables that change over time. Therefore, we can obtain unbiased estimates of the deter-
minants of math achievement. We believe a significant gap in the economics of education literature exists con-
cerning the use of panel techniques and our study is aimed at providing results to start filling this gap.
The related literature is surveyed in Section 2. Section 3 discusses the data, estimation procedures, variable
definitions, and the actual samples chosen. Section 4 reports the results of the estimations. The summary and
conclusions are presented in Section 5.
2. Literature review
As suggested by Hanushek 1986 and others,
5
rel- evant determinants of achievement include the student’s
innate characteristics along with the cumulative effects of her school, family, environment, and peers. In this
section the literature is reviewed which is related to the estimated models discussed in Section 4. In the dis-
cussion variables are grouped into two major categories: factors relating to schools and factors relating to the stud-
ent and his family. The schools category is further broken down into class size, teacher characteristics, time
on task, and type of school attended. Characteristics related to the family and individual are the family
income and marital status of the student’s parents, and the number of weekly hours the student works for pay.
2.1. School characteristics Characteristics of schools are used in most educational
production functions. 2.1.1. Class size
Teachers associations and educational policy makers have argued for smaller classes as a way of enhancing
learning in elementary and secondary schools. However, Hanushek 1986 reported that previous studies generally
found no relationship between class size and achieve- ment, and when they did the coefficient was not always
5
Another excellent and extensive survey of the early litera- ture prior to the early 1980s can be found in Glasman and Binia-
minov 1981. For more recent discussions see the Federal Reserve Bank of New York 1998.
263 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
in the expected direction. Findings in later studies also have been mixed. Cooper and Cohn 1997 found, for
mathematics achievement in South Carolina schools, that class sizes had no consistent effect on achievement.
Some coefficients were positive and some negative. On the other hand, Goldhaber and Brewer 1997 found a
positive and statistically significant relationship between class size and math achievement—larger class sizes were
associated with higher achievement Two studies have found smaller class size is associated with higher
achievement. Rouse 1998 in summarizing the current research on the effects on achievement of the Milwaukee
Parental Choice Program, suggests that the results are consistent with the hypothesis that children perform bet-
ter in small classes. Krueger 1997 using data from the Tennessee Student–Teacher Achievement Ratio STAR
experiment found that students did better in smaller classes. In summary, the findings in the literature are
mixed.
2.1.2. Teacher characteristics Hanushek 1986 reports prior to 1986 there had been
106 studies including teacher education, 109 studies including teacher experience, and 60 studies including
teacher salary as variables. The striking result from these early studies is the mixed nature of the effects. Ambigu-
ous results on these variables are also found in more recent studies.
6
Race and gender of the teacher and their association with achievement have been analyzed by several
researchers because the argument has been made that more teachers from under-represented groups should be
recruited to teach students from these under-represented groups. Because achievement and dropout rates of stu-
dents in these groups tend to be low and high respect- ively, compared to whites, some believe that teachers of
the same minority group would be better able to teach these students.
The teacher’s race and gender do not have consistent effects on achievement. Glasman and Biniaminov 1981
6
Dolan and Schmidt 1987 obtained a negative association of teachers salaries and reading achievement for 11th graders
but a positive association for 8th and 11th graders in math. Ehrenberg and Brewer 1994 found a positive and occasionally
significant relationship between achievement rates and expendi- tures per pupil for both black and white students.
Hanushek 1986 reported that although many studies found a positive coefficient for teacher experience, it was usually stat-
istically insignificant. Cooper and Cohn 1997 and Goldhaber and Brewer 1997 generally found a positive but statistically
insignificant relationship between teacher experience and math achievement. Hanushek 1992 found a statistically significant
and positive relationship for vocabulary and reading achieve- ment. Monk 1994 found both positive and negative coef-
ficients.
document the mixed coefficients on early studies. Recent studies that find lower achievement when a student’s
teacher is black include Cooper and Cohn 1997, Cohn and Teel 1991 and Goldhaber and Brewer 1997.
Ehrenberg, Goldhaber and Brewer 1995, found no sup- port for the hypothesis that the teacher’s race had any
significant impact on student achievement. Ehrenberg and Brewer 1994 found that an increase in the percent
of black faculty is associated with higher test scores.
Cooper and Cohn 1997, Cohn and Teel 1991, Ehrenberg et al. 1995 and Hanushek 1992 find that
the performance by female and male teachers is compa- rable when their effects on math achievement are con-
sidered. Although Goldhaber and Brewer 1997 found a positive relationship between the student having a female
teacher and math achievement, the general conclusion from the literature seems to be that variables which
reflect the race andor gender of a teacher are not usually significant determinants of student achievement. The
results for race and sex of the teacher are mixed. The general conclusion regarding the variables discussed to
date in the review is that no consistent results jump out of the past literature.
2.1.3. Time on task Zeith and Cool 1992 emphasize that the literature
consistently supports the importance of time spent on active learning as a determinant of academic achieve-
ment. Lewis and Seidman 1994 estimate that the amount of time a typical student spends on math in-
school and out-of-school by the 8th grade is 30 more in Japan than in the US. They conclude that a 21 day
increase in the length of the school year in the US, along with assigned homework during the summer, would
cause a major improvement in the performance of US students on achievement tests. The length of the school
year also is important because of evidence showing that students in the US forget substantial amounts of what
was learned during the year in the following summer and require about four weeks of review in the fall.
7
Krueger 1998 also emphasizes that the average school year in
the United States is shorter than in many other developed countries, and goes on to stress a well established fact
that more years of schooling are associated with higher
7
See New York State Department of Education 1978 Mor- ever, Entwisle, Alexander and Olson 1997 show that disad-
vantaged children lose ground during the summer while higher socioeconomic status SES students actually gain. Krueger
1998 interprets their results as suggesting that both high and low SES students have comparable gains during the school year
so that schools are offsetting the negative effects of low SES. However, during the summer months these negative effects
cause an increase in the gap between high and low SES stu- dents.
264 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
labor market earnings—something that should also apply to extending the length of the school year.
Gilby, Link and Mulligan 1993 utilized panel analy- sis on a sample of 8400 elementary students included in
the Sustaining Effects Study. They had observations on each student for three consecutive years and found that
extra hours of mathematics instruction per week are associated with small positive gains in mathematics
achievement.
Betts 1998 believes that increased expenditures per pupil and the increase in the minimum school leaving
age are two of the key reforms in public schooling in the US. He argues that these policies would have been
more effective had they been accompanied by increased educational standards. As he puts it
The missing ‘leg’ in these past reforms is a set of academic standards against which both students and
schools are measured. Betts, 1998, pp. 97–98
From the viewpoint of the present study, one important thing schools can do is heighten their expec-
tations of students. This can be done through a host of actions including stricter grading, curriculum standards
and assessment of whether the student is mastering the material, and additional homework. Policy makers must
recognize that achievement is influenced by the student’s own effort.
A comprehensive review of more than 100 studies in the literature relating to the effects of homework on aca-
demic outcomes of which achievement is only one can be found in Cooper 1989. Included in his review were
16 studies involving experiments where some students were placed in a group doing homework and others in a
group which did no homework. The overall evidence of these studies lends support to the hypothesis that home-
work enhances achievement. However, problems with many of these studies included the student assignment
strategies randomness of selection into groups and small sample sizes most involved one school and two
or less classes. Another literature surveyed by Cooper was denoted correlational. That is, how does the amount
of time spent on homework affect achievement as meas- ured by some test score. Results for 17 of these studies
are presented. Of these, nine utilized statistical tech- niques such as multiple regression analysis which con-
trolled for other variables such as family background and previous achievement. The findings generally support a
positive correlation between homework and achievement with at least one interesting difference. Homework
appears to have larger effects for junior high and high school students compared to elementary school students.
Because of data limitations, most of the earlier studies of homework had inadequate controls for previous
achievement. An exception is the study by Keith, Reim- ers, Fehrmann, Pottebaum and Aubey 1986 which had
detailed controls for prior achievement. The upshot of not controlling for previous achievement is the increased
probability of omitted variables bias. The only homework study we uncovered which util-
izes panel techniques is by Betts 1996. Analyzing the first 5 years of data from the Longitudinal Study of
American Youth, he found a positive association between the amount of homework assigned and student
achievement. Betts includes better controls for a stud- ent’s previous achievement. This control and the utiliz-
ation of panel techniques increases the likelihood that the estimated coefficient on the homework variable will
be unbiased. In conclusion, the evidence provides sup- port for increased homework as a means of increasing
test performance.
As was just noted, the literature on learning suggests that the more time spent studying math, in or out of class,
the higher will be math achievement. Other factors the same, the more a student watches TV during the week,
the less time there is for doing homework. Gortmaker, Salter, Walker and Dietz 1990 note that many studies
have found that increased time watching television is associated with a decline in achievement.
8
One of the main studies finding such a result is Keith et al. 1986
who used the first wave of the High School and Beyond Longitudinal Study to estimate the effects of TV time
on achievement. In conclusion, prior literature related to time on task supports the argument that more time spent
on mathematics, the higher should be the level of math- ematical achievement.
2.1.4. Type of school attended Utilizing the ‘High School and Beyond Study,’ Col-
eman and Hoffer 1987, Willms 1985 and Alexander and Pallas 1985 found positive effects associated with
attendance at Catholic schools and math achievement. However, the results of a study by Figlio and Stone
1997 based on the national educational longitudinal study found that Catholic school attendance did not
enhance achievement in the population as a whole.
Neal 1998, pp. 83–84 describes two points of caution when interpreting the previous literature on Catholic
school attendance as well as the results in the our study. First, none of the studies discussed above fully deals
with the fact that some students may be better suited for Catholic schools than others. It is hard to find evi-
dence that urban Catholic school students are simply better students than their public school counterparts
8
More recently, Glenn 1994 discussed the decline in vocabulary at most educational levels in the US. He attributes
this to a decline in the reading of newspapers and suggests that part of this decline in reading is due to an increase in the amount
of television time.
265 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
on some unobserved dimension. However, existing Catholic school students may be the students who
have the most to gain from Catholic schooling. We may be safe in concluding that Catholic schools pro-
vide real benefits for their current students. Much harder to ascertain is how many other students could
benefit from Catholic schooling if given the opport- unity. Would students from the Muslim families
benefit from Catholic schooling. Given the available data, we cannot answer this question. At best, we may
expect significant benefits from Catholic schooling for students who are quite similar to the existing
population of Catholic school students.
2.2. Characteristics of the family and student The home environment and economic status of a stud-
ent have always been recognized as important determi- nants of student achievement. As Hanushek 1986, p.
1163 states,
Virtually regardless of how measured, more educated and more wealthy parents have children who perform
better on average.
9
For example, Goldhaber and Brewer 1997 found a positive relationship between family income and math
achievement. An extensive literature exists regarding the effects of
divorce on the children in the household. The potential importance is highlighted by Emery and Forehand
1994 who point out that each year 2 of all children are in families going through a divorce, and 40 of chil-
dren aged 16 reside in a divorced family. Hopper 1997 in his extensive review of the general literature of the
effects of divorce on children enumerates several poten- tial negative effects. These include but are not limited
to, internalizing problems e.g. emotional difficulties, externalizing problems e.g. aggression, prosocial skills
e.g. social competence and also, difficulties in school which may be related to the other problems. It is the
potential negative effects on academic achievement tests that are of relevance to the present paper.
Divorce can have detrimental effects on children for at least two reasons. According to Hernandez and Myers
1995, p. 57 and other researchers, a short run effect of a divorce is a substantial drop in family income for many
children. Such a decline may require the mother go back
9
See Gyimah-Brempong and Gyapong 1991 for a justifi- cation for including family background as a determinant of
achievement. Pungello, Kupersmidt, Burchinal and Patterson 1996, provide a survey of the literature on the effects of low
income on student academic performance.
to work and at the same time lead to heightened tension in the relationship with the child. Moreover, and related
to the first point, with one parent removed from the household, children may receive less care and attention
each day than would have been the case in a two par- ent family.
Amato and Keith 1991a,b and Forehand, Armistead and Klein 1995 provide surveys of the literature regard-
ing divorce and student achievement which cover more than 40 studies of the issue. When analyzing the effects
of divorce on a child’s achievement, Amato and Keith 1991a found that students from divorced families score
lower on measures of academic achievement by about one-sixth of a standard deviation when compared to chil-
dren from intact families. Amato and Keith 1991b, however, noted that even though significant in the stat-
istical sense, the sizes of the effects would be considered trivial by many educational researchers. Forehand,
Armistead and Klein 1995, p. 256 summarize the litera- ture in the following statement.
In conclusion, parental divorce is related to multiple areas of children’s school performance. However,
contrary to the image portrayed in the public media, the scientific data suggest that the magnitude of these
effects, as well as effects in settings other than school, is relatively small. p. 256
Their explanation of this overall conclusion is based on three major points. First, divorce may well be a pain-
ful experience for youngsters but it apparently does not hurt their ability to function in school Emery Fore-
hand, 1994. Second, some students are probably affec- ted negatively by divorce but others are not. Or, as they
put it
Therefore, one should not conclude that divorce is harmless—or that it is so harmful that all children
should automatically receive psychological treatment. Forehand et al., 1995.
Finally, and related to the previous point, it is not div- orce itself but the conditions in the home that go along
with such a situation that affect a child’s ability to func- tion Amato, 1993.
The panel nature of the NELS data and associated panel estimation techniques used in the current study
should provide controls for the accompanying factors just noted. Based on the divorce literature, we do not
expect divorce to have a large effect on the math achievement of high school students.
10
10
However, negative results are not guaranteed. Marsh 1990, using the High School and Beyond Study HSB found
no effects on achievement due to family dissolution. Mulkey, Crain and Harrington 1992 found negative effects of divorce
on vocabulary and science tests although the effects of dissol-
266 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
Many students are involved with part time work while in high school. Primarily, students are involved in labor
market activity to provide money for current living expenses and discretionary items. Most studies have
found negative associations of student work with aca- demic performance and subsequent educational attain-
ment.
11
Interestingly, this variable should provide an excellent indicator of student motivation.
3. Data and methodology
